Quantum Channel Construction with Single-Ancilla Binary Trees

The patent segments the construction of arbitrary CPTP maps into a binary-tree structure where the quantum channel is built through hierarchical decomposition. Instead of requiring all ancilla qubits simultaneously, the method divides the operation into stages corresponding to tree levels, where each level processes a subset of the transformation. This segmentation reduces the peak number of ancilla qubits needed while maintaining the ability to construct any arbitrary quantum channel.

The patent transforms the problem from a direct high-dimensional quantum operation into a sequence of lower-dimensional operations organized in a binary-tree structure. By introducing the temporal dimension of sequential operations and the structural dimension of the binary tree, the method achieves arbitrary CPTP map construction with reduced spatial resources (fewer ancilla qubits) and optimized circuit depth scaling.

The binary-tree structure segments the quantum channel construction into logarithmic stages rather than linear sequential operations. Each level of the binary tree represents a stage that can be executed in parallel or with minimal sequential overhead, reducing the total circuit depth from linear scaling O(d) to logarithmic scaling O(log d) where d is the qudit dimension.

The method performs preliminary organization of the CPTP map into Kraus operators and structures them according to the binary-tree hierarchy before execution. This preliminary arrangement enables efficient parallelization and reduces the sequential depth required during actual quantum circuit execution, as the computational structure is already optimized for the target architecture.